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Theoretically, theapplication of three or four implants creates an angularrelationship between the implants instead of a straight-linerelationship. In the three-implant-supported overdenture, themost anteriorly positioned implant may provide indirectretention for the denture by preventing the intrusion of theanterior portion of the denture towards the tissues.14Therefore, it has been recommended by some authors thatclinicians should use three or four implants in situations thatrequire increased retention, such as high muscle attachmentor prominent mylohyoid ridges.15However, in general, the useof mandibular overdentures supported by more than twoimplants does not lead to greater patient satisfaction in termsof denture and social function. Meijer et al. found no cleardifference in either clinical or radiographic outcomes betweentwo-implant-retained and four-implant-supported mandibu-lar overdentures over a 10-year evaluation period.16Mericske-Stern compared the clinical results between two-, three- andfour-implant mandibular overdentures and proposed that twoimplants can adequately serve as retention for a completemandibular denture.17For reasons of cost-effectiveness,Meijer et al. proposed that a two-implant overdenture isadvisable for patients with Cawood classes IV–VI resorption ofthe mandible and complaints concerning retention andstability of the lower denture.16Besides retention, it is also of vital importance not to causeexcessive load on implants.18In natural teeth, the periodontalligament acts as an intermediate cushion to buffer the occlusalloads.19However, in the osseointegrated dental implant,occlusal loads are transmitted directly to the surroundingbones. When overloading happens, high deformations (above2000–3000 microstrain) occur in the bone around the implants.When pathological overloading occurs (over 4000 microstrain),stress and strain gradients exceed the physiological limits of thebone, which may cause micro-fractures at the bone–implantinterface, fracture of the implant, loosening of components ofthe implant system, and unwanted bone resorption.20,21Recognizing the damage done by overloading, clinicianspay close attention to the stress and strain developed in peri-implant bone when using different prosthetic designs. Three-dimensional finite element analysis (3D FEA) has beenconsidered a precise and appropriate approach for investigat-ing stress and strain distribution in bone and offers manyadvantages over other methods in simulating the complexityof clinical situations.22To date, there has been little previousresearch comparing the stress or strain in peri-implant boneusing mandibular overdentures retained by different numbersof implants. Therefore, the main goal of this study was tocompare through 3D FEA the strain distributions in peri-implant bone, stress in the abutments and denture stability ofmandibular overdentures retained by one, two, three, or fourimplants.2. Materials and methods2.1. Model designTo obtain the geometry of a totally edentulous patient’smandible, a computed tomography (CT) examination wascarried out on a volunteer, with approval from the ethnicalcommittee of Peking University School of Stomatology(IRB00001052-07051). Her mandible and mandibular over-denture were scanned. The CT examination files were thenimported into Mimics8.0 (Materialise, Leuven, Belgium).Straumann implants (Straumann, Basel, Switzerland; diame-ter: 4.1 mm, length: